Limit Summary
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AP Calculus Names: Limit Summary Group Assignment Show all work on a separate sheet of paper!!!! State which method (substitution, numeric, algebraic, and/or graphical representation) you used to solve the problem and why you chose that approach. y −1 = y −1
1. lim y →1
3. a. lim h →0
2. lim x →1
( 2 + h) 2 − 4 2
25 − x 2 − 4
4. lim x →3
x−3
=
b. lim h →0
( 2 + h) 2 − 4 h
x3 −1 = x −1
=
f ( x ) − f (1) = x −1
5. lim x →1
=
f ( x) = x 2 − 2x + 3
6. lim x →0
1 = x2
7. lim x →0
x
8. lim x →∞
x2 +1 = 1 − 2x 2
9. lim x →∞
x2 +1 = 1− x
10. lim x →∞
12. lim x →0
1 − 2x = x + x +1
1 − cos x = x
−
x →1
15. lim x →0
11. lim x →0
2
14. a. lim
1− x 1− x
sin 8 x = x
=
x
=
sin x = x
x 2 + 5x − x = 13. lim x →∞
b. lim +
x →1
1− x 1− x
=
1. lim y →1
3. a. lim h →0
2. lim x →1
( 2 + h) 2 − 4 2
25 − x 2 − 4
4. lim x →3
x−3
=
b. lim h →0
( 2 + h) 2 − 4 h
x3 −1 = x −1
=
f ( x ) − f (1) = x −1
5. lim x →1
=
f ( x) = x 2 − 2x + 3
6. lim x →0
1 = x2
7. lim x →0
x
8. lim x →∞
x2 +1 = 1 − 2x 2
9. lim x →∞
x2 +1 = 1− x
10. lim x →∞
12. lim x →0
1 − 2x = x + x +1
1 − cos x = x
−
x →1
15. lim x →0
11. lim x →0
2
14. a. lim
1− x 1− x
sin 8 x = x
=
x
=
sin x = x
x 2 + 5x − x = 13. lim x →∞
b. lim +
x →1
1− x 1− x
=
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